The line 2x + 3y = 12 touches the ellipse x^2/9 + y^2/4 = 2 at the point (3, 2).

Question

State whether the statements True or False. Justify

The line 2x + 3y = 12 touches the ellipse x²/9 + y²/4 = 2 at the point (3, 2).

Answer 1

4x² + 9y² = 72 & 2x + 3y = 12

Solving both the expressions,

2x = 12 – 3y

Squaring both sides,

(2x)² = (12 – 3y)²

4x² = (12 – 3y)²

Putting the value of 4x²,

(12 – 3y)² + 9y² = 72

144 + 9y² - 72y + 9y² - 72 = 0

18y² - 72y + 72 = 0

Y² - 4y + 4 = 0

(y – 2)²= 0

y = 2

2x = 12 – 3y

2x = 12 – 3(2)

2x = 12 – 6 = 6

x = 3

So, the point of intersection is (3,2).

TRUE